Japanese Patent publication No. 11-125151 (referred to as patent document 1, hereinafter) shows the exhaust gas recirculation system (referred to as EGR system) which recirculates a part of an exhaust gas (referred to as EGR gas) exhausted from an engine to an intake side of the engine. In the exhaust gas recirculation system, it is required to control the EGR gas to an appropriate temperature, when the EGR gas is recirculated to the intake side. The exhaust gas recirculation system preforms a heat exchange between an engine cooling water and the EGR gas in an EGR cooler. When the temperature of the engine cooling water is low, the temperature of the engine cooling water is heated above the dew point temperature of the EGR gas by a combustion heater. Accordingly, a generation of sulfuric acid caused by gaseous components dissolving into dew condensed EGR gas can be suppressed. The exhaust gas recirculation can be carried out before a warming-up of the engine is completed, and the effect of reducing nitrogen oxides can be obtained at an early stage.